A new simultaneous extension method for B-spline curves blending with G2-continuity

Curve blending is an extremely common problem in CAD systems. The current blending methods were looking for a third curve to join curves and some of the methods needed to distinguish the transition curve were C-or S-shaped. In this paper, we study a simultaneous extension method to blend curves with G2-continuity. The method simultaneously extends the two curves at one of their endpoints and makes them intersect at a common joint under geometric constraints. The basic concept of B-spline curves and its extension theory is presented firstly. Then we propose the blending algorithm of simultaneous extension. This method does not need to prejudge the shape of transition curves, which is, without considering the placement of two original curves and reduces the number of blending joints from two to one. Four curve blending examples are presented to verify the validity of the new method.